These books are the most important ones for pre-electronic and zeroth/first generation electronic:
Nicholas Metropolis, J. Howlett, Gian-Carlo Rota, (editors), A History of Computing in the Twentieth Century (Academic Press, New York, 1980)
Brian Randell, (editor), The Origins of Digital Computers (Springer-Verlag, Berlin, 1973)
General
These are less important (arranged by period/topic):
Michael R. Williams, A History of Computing Technology, (Prentice-Hall, Englewood Cliffs, 1985)
William Aspray, John von Neumann and the Origins of Modern Computing, (MIT Press, Cambridge, 1990)
Herman H. Goldstine, The Computer from Pascal to Von Neumann (Princeton University Press, 1972)
B. V. Bowden, (editor), Faster than Thought, (Pitman, 1975)
Simon H. Lavington, Early British Computers: The Story of Vintage Computers and The People Who Built Them (Manchester University Press, 1980)
Simon H. Lavington, A History of Manchester Computers, (National Computer Center, Manchester, 1975)
M. D. Fagen (editor), National Service in War and Peace (1925-1975), Volume II of A History of Engineering and Science in the Bell System (Bell Telephone Laboratories, 1978)
David M. Yates, Turing's Legacy: A History of Computing at the National Physical Laboratory, 1945-1995 (Science Museum, London, 1997)
Arthur L. Norberg, Judy E. O'Neill, Kerry J. Freedman, Transforming Computer Technology: Information Processing for the Pentagon, 1962-1986 (Johns Hopkins University, Baltimore, 1996)
Adele Goldberg, History of Personal Workstations (Addison Wesley Professional, Boston, 1988) Also covers some early machines, e.g. the LINC
Specific topics
These cover specific computers/companies:
B. E. Carpenter, R. W. Doran, A. M. Turing's ACE Report of 1946 and Other Papers, (MIT Press, Cambridge, 1986)
Emerson W. Pugh, Memories That Shaped an Industry: Decisions Leading to IBM System/360 (MIT Press, Cambridge, 1984)
Charles J. Bashe, Lyle R. Johnson, John H. Palmer, Emerson W. Pugh, IBM's Early Computers (MIT Press, Cambridge, 1986)
Emerson W. Pugh, Lyle R. Johnson, John H. Palmer, IBM's 360 and Early 370 Systems (MIT Press, Cambridge, 1991)
C. Gordon Bell, J. Craig Mudge, John E. McNamara, Computer Engineering: A DEC View of Hardware Systems Design (Digital, 1979)
Werner Buchholz (editor), Planning a Computer System: Project Stretch (Mcgraw-Hill, New York, 1962)
Jim E. Thornton, Design of A Computer: The Control Data 6600 (Scott, Foresman, Glenview, 1970)
Biographies - individuals
Relevant biographies:
Andrew Hodges, Alan Turing: The Enigma (Simon and Schuster, New York, 1983) The definitive bio of him; although there are a couple of later ones which include some recently-released classified info which wasn't in this one, they are short and poorly sourced, so this is still the preferred one.
Maurice Wilkes, Memoirs of a Computer Pioneer (MIT Press, Cambridge, 1985)
Herman Lukoff, From Dits to Bits: A Personal History of the Electronic Computer (Robotics, Portland, 1979)
David E. Lundstrom, A Few Good Men from Univac (MIT Press, Cambridge, 1987)
Biographies - group
Gareth Ashurst, Pioneers of Computing (Frederick Muller, London, 1983)
David Ritchie, The Computer Pioneers: The Making of the Modern Computer (Simon and Schuster, New York, 1986)